dtan5457
  • dtan5457
If y^-3x=27, compute exactly 7^2x+1
Mathematics
jamiebookeater
  • jamiebookeater
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dan815
  • dan815
y^(-3x)=27, compute exactly 7^(2x)+1?
dtan5457
  • dtan5457
7^(2x+1)
Jhannybean
  • Jhannybean
So then you need to figure out x and then plug that x-value into \(7^{2x}+1\) ?

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dtan5457
  • dtan5457
the +1 is part of the exponent
dtan5457
  • dtan5457
and yes i believe so
dan815
  • dan815
infinite solutions
dtan5457
  • dtan5457
what would be the steps to attempt to solve this though
dan815
  • dan815
|dw:1443998600989:dw|
Jhannybean
  • Jhannybean
OK dan can you help me for a sec
Jhannybean
  • Jhannybean
How do you make the exponent of y positive without putting it over 1
dan815
  • dan815
|dw:1443999336822:dw|
Jhannybean
  • Jhannybean
Ohh!! got it.
Jhannybean
  • Jhannybean
wow that was dumb lol.
freckles
  • freckles
\[\text{If } y^{-3x}=27, \text{ compute exactly } 7^{2x+1} \] Are we given anything else? Like are we given any restrictions on x and y?
dtan5457
  • dtan5457
no thats all is given
freckles
  • freckles
\[y^{-3x}=27 \\ y^{3x}=\frac{1}{27} \\ y^{3x}=3^{-3} \\ \ln(y^{3x})=\ln(3^{-3}) \\ 3x \ln(y)=\ln(3^{-3}) \\ 3x \ln(y)=-3 \ln(3) \\ \text{ solve for } x \\ \text{ then replace } x \text{ in } 7^{2x+1}\]
freckles
  • freckles
instructions seem weird it seems like it is looking for like a constant value
Jhannybean
  • Jhannybean
\[\frac{1}{y^{3x}} = 27 \]\[ y^{3x} = \frac{1}{27}\]\[\ln(y^{3x}) = \ln\left(\frac{1}{27}\right)\]\[3x\ln(y)=-\ln(27)\]\[\ln(y)=-\frac{\ln(27)}{3x}\]\[e^{\ln(y)} =e^{-\frac{\ln(27)}{3x}}\]\[y=e^{-\frac{\ln(y)}{3x}}\]
Jhannybean
  • Jhannybean
darnit, took me forever to write out in latex :\ bummer
freckles
  • freckles
but as @dan815 said it isn't
dtan5457
  • dtan5457
its alright ill just skip this question until my teacher can explain it tomorrow
dtan5457
  • dtan5457
thanks guys
Jhannybean
  • Jhannybean
typo, meant to write \(\ln(27)\) and i wrote \(ln(y)\) lol.
freckles
  • freckles
this is question come from a book @dtan5457
dtan5457
  • dtan5457
no just a worksheet written by my teacher
freckles
  • freckles
would it be difficult for you to post an attachment of it here?
dtan5457
  • dtan5457
im not sure about that as my scanner cant be used at the moment but ill probably have a few more questions from it later
freckles
  • freckles
ok
dtan5457
  • dtan5457
none of the questions are directly similar but its all pre calc and some trig
freckles
  • freckles
this is prettiest I can make it \[7^{\log_y(\frac{y}{9})}\] but I don't know if it matches the directions to "compute exactly"

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